Boing this is what I get for staying up late. I don't know where my head was, but for some reason I thought you had seperate GPU already.
So as groundrat said, you'll need some kind of additional GPU to run 3 screens, just the mobo GPU won't suffice, as it supports a maximum of two simultaneous monitors.
So if you want to just extend to a third screen for productivity, any cheap GPU will do. However gaming won't be an option.
If you want to game then again as groundrat said a 7870 or higher would be preferred.
Lastly to your question can you swap between eyefinity and extended screen modes? Absolutely. You literally press two keys to swap between the two modes.
Nvidia also offers 3 monitor gaming nowadays using a single card.